In this article, we will discuss what is a percentage and how to calculate it. So, let us get started.

Percentage

A ratio or a number that depicts a part or fraction of 100 is known as a percentage. We often use the word percent to describe the percentage and denote it by the symbol %.

When we use the word percent, we actually mean value of something per hundred. For example, 25 percent is equal to \frac{25 } {100} and 100 percent is equal to \frac{100}{100} = 1.

A percentage can be represented as a fraction or a decimal number. For instance, 78% is equal to 0.78 or \frac{78} {100}.

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How to calculate the percentage

We multiply the numeric value of the ratio by 100 to get a percentage. For example, suppose there are a total of 30 marbles in a basket. John gets 10 of them and his younger sister gets 20 of them. What percentage of marbles both of them have?

Well, first we need to find out the ratio. The ratio of marbles John have is \frac{10}{30}. Now, we will multiply this ratio by 100 to get the percentage of marbles he gets.

= \frac {10}{30} \times 100%

= 33.33 %

Hence, John gets 33.33% of the total marbles.

To calculate the percentage of marbles his younger sister gets, we will simply subtract 33.33% from 100%.

= 100% - 33.33% = 66.67%

In the next section of the article, we will solve a couple of examples related to percentage.

 

Example 1

The cost of a motorbike was $5000 last month. The same motorbike is available at a 25% discount this month. What is the new cost of the motorbike?

Solution

The cost of the motorbike last month = $5000

Percent discount = 25%

Discount (in dollars) = \frac{25}{100} \times 5000

= $1250

The new cost of the motorbike = $5000 - $1250 = $3750

 

 Example 2

The price of an apartment last year was $85000. In this year, the price is increased by 15%. What is the new cost of the apartment?

Solution

Initial price of the apartment = $85000

Percent increase in the price = 15%

Increase in the price by dollars = \frac{15}{100} \times 85000

= $12750

New price of the apartment = $85000 + $12750

= $97750

 

Example 3

The cost of the furniture was $1500 last month. The same furniture costs $1200 this month. Calculate the percent decrease in the cost of the furniture.

Solution

The cost of the furniture last month = $1500

New cost of the furniture = $1200

Percent decrease in the cost = 100% - \frac{1200}{1500} \times 100%

= 100% - 80% = 20%

Hence, there is 20% reduction in the price of the furniture this month.

 

Example 4

There are 50 students in the class. 17 out of 50 students like mathematics, 23 students like computer science, and the rest of the students like physics. What percentage of students like mathematics, computer science, and physics?

Solution

Total students in the class = 50

Number of students who like mathematics = 17

Percentage of students who like mathematics = \frac{17}{50} \times 100%

= 34%

Number of students who like computer science = 23

Percentage of students who like computer science = \frac{23}{50} \times 100%

= 46%

Number of students who like physics = 50 - (17 + 23) = 10

Percentage of students who like physics = \frac{10}{50} \times 100% = 20%.

 

Example 5

There are 200 students in a college. 56 out of 200 students like to play football, 85 students like basketball, and the rest of the students like both football and basketball. What percentage of students like football, basketball, and both the games?

Solution

Total students in a college = 200

Number of students who like football = 56

Percentage of students who like football = \frac{56}{200} \times 100%

= 28%

Number of students who like basketball = 85

Percentage of students who like basketball = \frac{85}{200} \times 100%

= 42.5%

Number of students who like both the games = 200 - (56 + 85) = 59

Percentage of students who like both the games = \frac{59}{200} \times 100% = 29.5%.

 

Example 6

The total pocket money of Sarah, John, and Alice are $500, $800, and $600 respectively. In this month, Alice got 12% more pocket money, John received 25% less pocket money, and Alice got $150 more than the previous month.

a) How much pocket money did Sarah get this month?

b) How much pocket money did John get this month?

c) Calculate the percent increase in the pocket money of Alice this month?

Solution

This question has three parts. We will solve each part separately one by one.

Part a

Total pocket money Sarah got last month = $500

Percentage increase in her pocket money this month = 12%

Total pocket money Sarah got this month = $500 + \frac{12}{100} \times 500

= $560

Hence, Sarah got $560 this month.

 

Part b

Total pocket money John received last month = $800

Percent decrease in his pocket money this month = 25%

Total pocket money John received this month = $800 - \frac{25}{100} \times 800

= $600

Hence, John received $600 this month.

 

Part c

Total pocket money of Alice last month = $600

Pocket money after increase (in dollars) = $600 + $150 = $750

Percent increase in the pocket money = \frac{150}{600} \times 100% = 25%

 

Example 7

Out of 120 questions in a test, John gets 75% correct. How many questions did he answer incorrectly in the test?

Solution

Total questions in a test = 120

Percentage of correct answers = 75%

Number of questions answered correctly = \frac{75}{100} \times 120 = 90

Hence, he answered 90 questions correctly

Number of questions he answered incorrectly = Total number of questions - Number of questions answered correctly

= 120 - 90 = 30

Hence, John answered 30 questions incorrectly.

 

Example 8

Out of 250 questions in an exam, John attempts 80% of the total questions. Out of the attempted questions, 150 of his answers are correct, and the remaining are wrong.

a) How many questions did he attempt and missed in the exam?

b) What percentage of total questions, did he answer correctly?

c) What percentage of total questions did he answer incorrectly?

Solution

This question has 3 parts. We will solve each part separately.

Part a

Total questions in an exam = 250

Percentage of questions John attempted = 80%

Number of questions he attempted = \frac{80}{100} \times 250 = 200 questions

Hence, he attempted 200 questions in the exam.

Number of questions missed in the exam = Total questions - Number of questions attempted

= 250 - 200 = 50 questions

Hence, he missed 50 questions in the exam.

 

Part b

Number of correct answers = 150

Total number of questions in the exam = 250

Percentage of correct answers = \frac{150}{250} \times 100% = 60%

 

Part c

Number of incorrect answers = 200 - 150 = 50

Total number of questions in the exam = 250

Percentage of incorrect answers = \frac{50}{250} \times 100% = 20 %

 

Example 9

In a college, 30% of the total teachers teach physics. If the number of teachers in a college who teach physics is 45, then how many total teachers are there in a college?

Solution

Number of teachers who teach physics = 45

Percentage of teachers who teach physics = 30%

In other words, we can say that the number of physics teachers is 0.30 times the total number of teachers. The formula can be written as:

Number of physics teachers = Total number of teachers x 0.30

We can derive the formula for the total number of teachers from the above formula like this:

Total number of teachers = \frac{Number of physics teachers} {0.30}

Total number of teachers in the college = \frac{45} {0.30} = 150

Hence, the total number of teachers in a college is 150.

 

Example 10

In a class, 40% of the total students enrolled for the extra class. If the number of students who enrolled for an extra class is 24, then how many total students are there in a class?

Solution

Number of students who enrolled for the extra class= 24

Percentage of students who got enrolled for an extra class = 40%

In other words, we can say that the number of students who enrolled themselves for an extra class is 0.40 times the total number of students in the class

Number of students who got enrolled = Total number of students in a class x 0.40

We can derive the formula for the total number of teachers from the above formula like this:

Total number of students in the class = \frac{Number of students who enrolled for an extra class} {0.40}

Total number of students in a class = \frac{24} {0.40} = 60

Hence, the total number of students in the class is 60.

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Rafia Shabbir